C. C. Centeno ; S. Dantas ; M. C. Dourado ; Dieter Rautenbach ; Jayme Luiz Szwarcfiter - Convex Partitions of Graphs induced by Paths of Order Three

dmtcs:502 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, Vol. 12 no. 5 - https://doi.org/10.46298/dmtcs.502
Convex Partitions of Graphs induced by Paths of Order ThreeArticle

Authors: C. C. Centeno 1; S. Dantas 2; M. C. Dourado 1; Dieter Rautenbach 3; Jayme Luiz Szwarcfiter 1

  • 1 Instituto de Matemática da Universidade Federal do Rio de Janeiro
  • 2 Instituto de Matematica [Fluminense]
  • 3 Institut für Optimierung und Operations Research

A set C of vertices of a graph G is P(3)-convex if v is an element of C for every path uvw in G with u, w is an element of C. We prove that it is NP-complete to decide for a given graph G and a given integer p whether the vertex set of G can be partitioned into p non-empty disjoint P(3)-convex sets. Furthermore, we study such partitions for a variety of graph classes.

https://doi.org/10.46298/dmtcs.502
Source: HAL:hal-00990463v1
Volume: Vol. 12 no. 5
Section: Graph and Algorithms
Published on: January 1, 2010
Imported on: March 26, 2015
Keywords: graph convexity,convex partition,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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